Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013 (2013), Article ID 582532, 9 pages.
Infinitely Many Elliptic Solutions to a Simple Equation and Applications
Based on auxiliary equation method and Bäcklund transformations, we present an idea to find infinitely many Weierstrass and Jacobi elliptic function solutions to some nonlinear problems. First, we give some nonlinear iterated formulae of solutions and some elliptic function solutions to a simple auxiliary equation, which results in infinitely many Weierstrass and Jacobi elliptic function solutions of the simple equation. Then applying auxiliary equation method to some nonlinear problems and combining the results with exact solutions of the auxiliary equation, we obtain infinitely many elliptic function solutions to the corresponding nonlinear problems. The employed approach is powerful and can be also applied to solve other nonlinear differential equations.
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 582532, 9 pages.
First available in Project Euclid: 27 February 2014
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Wei, Long; Wang, Yang. Infinitely Many Elliptic Solutions to a Simple Equation and Applications. Abstr. Appl. Anal. 2013 (2013), Article ID 582532, 9 pages. doi:10.1155/2013/582532. https://projecteuclid.org/euclid.aaa/1393511994